Competition and multi-agent search with overlapping spaces

Investigate competitive and multi-agent versions of the continuum-arm problem-solving model with overlapping search spaces and informational spillovers, and characterize how competitive pressure shapes agents’ equilibrium breadth and depth of search, their selection of approaches, and the resulting balance between duplication and diversity of effort.

Background

The paper develops a dynamic model of problem solving under unknown difficulty and a tractable continuum formulation in which an agent chooses search breadth and depth. All main results are derived in single-agent settings. Extending this framework to strategic environments with multiple agents requires specifying how agents’ search spaces overlap and how their outcomes and information spill over across agents.

The discussion suggests that competition could meaningfully alter exploration choices (e.g., whether to pursue distinct approaches versus duplicating others’ efforts) and that richer cross-agent informational spillovers would be crucial to capture duplication versus diversity in scientific and technological races.

References

Several avenues for future research remain open. First, examining competitive and multi-agent environments with overlapping search spaces would shed light on the interplay between competitive pressures and what approaches agents choose to pursue. Extending the continuum model to allow for richer informational spillovers across agents could shed light on the balance between duplication and diversity of effort in scientific and technological races.

— Solving Problems of Unknown Difficulty  (2604.00156 - Wu, 31 Mar 2026) in Section 6: Discussion and Future Work

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— Turn-Based Combat Arena: A New Framework for Multiagent Training and Game Balancing  (2609.03122 - Vasyuta et al., 2 Sep 2026) in Introduction

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— Photonics-GCCE: group collaborative-competitive evolution multi-agent framework for universal and autonomous optical design  (2609.28045 - Xu et al., 23 Sep 2026) in Introduction